It definitely does! Two actually. But It’s also pretty overkill for use in an arduboy, imo. I tend to use cheap charging circuits from old vapes, but if you want to source compnents from online instead of salvage, adafruit has a couple other chargers that should be perfect. This one is neat because the usb connections are part of the PCB, though they could easily be brought out if this was an inconvenient form factor. This one is just a basic chrager circuit that would be perfect for a pro micro. Both are WAY cheaper than the powerboost 500 and will work just as well.
Are you having to reburn the bootloader every single sketch or just once when you first use them? Sometimes pro micros will be shipped with a different bootloader than the standard arduino core for whatever reason, and you have to burn the correct bootloader onto them so that it works. However, you should only have to do this once when you first get it if you are having issues with it. I don’t think opting for the expensive name-brand is going to change much, they might just have the correct bootloader on them but really you’ll be paying for a label and some red pcb more than anything. The big issue with clones is that they use some lower quality connectors, the micro-usb port tends to come off easily as it’s only a surface-mount connector instead of having through-hole stabilizers.
Those schematics are fine but you may find these more useful and easier to follow. For the 3pin switch it’s up to you how you want your charger and arduboy to behave, but can be as simple as connecting the switch’s middle pin between the charger’s negative(-) output and the battery’s negative(-) wire, and connecting one of the side pins to your pro micro’s GND. When turned on you can and use the battery, when not it should charge.
RGB LED has 4 legs, the longest one is your common, it should be second to last from the side with a flat edge. The arduboy uses common anode which is a positive(+) lead. Connect the common anode to pro micro’s VCC. I’ve also seen people use common cathode paired with a level shifter IC, but doesn’t seem worth it imo.
I don’t know if you’ve used the RGB before, but do NOT just connect everything. It will burn out extremely fast. Each of the leds inside the led (I know, but stay with me, it’s just how it works) requires a different amount of current to safely activate it. over a certain amperage and they’ll just burn and be more useless than a paperweight. You must attach resistors to each of the pins EXCEPT common anode. Most people go with specific resistances for each color to get consistent brightness across all three. Personally, this is a waste of time when it comes to arduboy, and 3 resistors that are around 220-330ohms should be perfect, but you can probably get away with whatever you have on-hand as long as it’s at least 100ohms and less than 1kohms.